Wasowicz, Szymon On quadrature rules, inequalities and error bounds. (English) Zbl 1179.41031 JIPAM, J. Inequal. Pure Appl. Math. 9, No. 2, Paper No. 36, 4 p. (2008). The author considers six operators approximating the integral mean value \(\frac{1}{2}\int_{-1}^{1}f(x)dx.\) All of them are connected with the very well known rules of approximate integration: Chebyshev quadrature, Gauss-Legendre quadrature with two and three knots, Lobatto quadrature with four and five knots and Simpson’s rule.In this paper the order structure of the set of these six operators is established in the class of 5-convex functions. An error bound of the Lobatto quadrature rule with five knots is given for less regular functions as in the classical result. Reviewer: Ana-Maria Acu (Sibiu) Cited in 1 Document MSC: 41A55 Approximate quadratures 26A51 Convexity of real functions in one variable, generalizations 26D15 Inequalities for sums, series and integrals Keywords:approximate integration; quadrature rules; convex functions of higher order PDFBibTeX XMLCite \textit{S. Wasowicz}, JIPAM, J. Inequal. Pure Appl. Math. 9, No. 2, Paper No. 36, 4 p. (2008; Zbl 1179.41031) Full Text: arXiv EuDML EMIS